Quadratic momentum dependence in the nucleon-nucleon interaction

We investigate different choices for the quadratic momentum dependence required in nucleon-nucleon potentials to fit phase shifts in high partial waves. In the Argonne v₁₈ potential L² and (L·S)² operators are used to represent this dependence. The v₁₈ potential is simple to use in many-body calculations since it has no quadratic momentum-dependent terms in S waves. However, p² rather than L² dependence occurs naturally in meson-exchange models of nuclear forces. We construct an alternate version of the Argonne potential, designated Argonne v_18pq, in which the L² and (L·S)² operators are replaced by p² and Q_ij operators, respectively. The quadratic momentum-dependent terms are smaller in the v_18pq than in the v₁₈ interaction. Results for the ground-state binding energies of ³H, ³He, and ⁴He, obtained with the variational Monte Carlo method, are presented for both the models with and without three-nucleon interactions. We find that the nuclear wave functions obtained with v_18pq are slightly larger than those with v₁₈ at interparticle distances <1 fm. The two models provide essentially the same binding in the light nuclei, although v_18pq gains less attraction when a fixed three-nucleon potential is added.